INSTITUTE OF AERONAUTICAL ENGINEERING

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1 INSTITUTE OF AERONAUTICAL ENGINEERING DUNDIGAL , HYDERABAD COMPUTER SCIENCE AND ENGINEERING TUTORIAL QUESTION BANK Course Name : FORMAL LANGUAGES AND AUTOMATA THEORY Course Code : A40509 Class : II B. Tech II Semester Branch : Computer Science and Engineering Year : Course Faculty : Dr K Rajendra Prasad, Professor Ms N Mamatha, Assistant Professor Ms M Sandhya Rani, Assistant Professor Ms T Ramya, Assistant Professor OBJECTIVES To meet the challenge of ensuring excellence in engineering education, the issue of quality needs to be addressed, debated and taken forward in a systematic manner. Accreditation is the principal means of quality assurance in higher education. The major emphasis of accreditation process is to measure the outcomes of the program that is being accredited. In line with this, Faculty of Institute of Aeronautical Engineering, Hyderabad has taken a lead in incorporating philosophy of outcome based education in the process of problem solving and career development. So, all students of the institute should understand the depth and approach of course to be taught through this question bank, which will enhance learner s learning process. Group - A (Short Answer Questions) S. No. Questions Blooms Taxonomy Level UNIT - I Part- A (Short Answer Questions) 1. Explain transition diagram, transition table with example. Understand 1. Define transition function of DFA. Remember 3. Define ε transitions. Remember 4. Construct a DFA to accept even number of 0 s. 5. Define Kleene closure and positive closure. Remember 1 6. Construct a DFA to accept empty language. 7. Explain power of an alphabet ( *)? Understand 1 8. Write transition diagram for DFA accepting string ending with 00 defined over an alphabet = {0,1} 9. Write transition diagram for DFA to accept exactly one a defined over an alphabet = {a,b} 10. Define NFA with an example. Remember 11. Explain the different Operations on the languages. Understand 1. Construct a finite automaton accepting all strings over {0, 1} having even number of 0 s Course Outcomes

2 13. Define Moore Machines. Remember Define Mealy Machines. Remember Write DFA for odd number of 1 s. 16. Write NFA for (0+1)*101(0+1)*. 17. Write DFA for (0+1)*10(0+1)*. 18. Define ɛ - closure. Remember 19. Write NFA for (0+1)*001(0+1)*. 0. Write DFA for (0+1)*00(0+1)*. 1 Define FSM and its structure with an example. Remember Give any two comparisions between NFA and DFA Remember Part- B (Long Answer Questions) 1. Construct a DFA to accept set of all strings ending with 010. Define language over an alphabet = { 0,1} and write for the above DFA.. Construct a Moore machine to accept the following language. L = { w w mod 3 = 0} on = { 0,1,} 3 3. Write any six differences between DFA and NFA 4. Write NFA with Ɛ to NFA conversion with an example. Understand 5. Construct NFA for (0 + 1)*( )(0 + 1)* and Convert to DFA. 6. Design DFA for the following languages shown below = { a,b} a) L={w/ w does not contain the substring ab} b) L={w/ w contains neither the substring ab nor ba} c) L={w/ w is any string that doesn t contain exactly two a} d) L={w/ w is any string except a and b} 7. Illustrate given FA s are equivalent or not with an example Construct Mealy machine for (0 + 1)*( ) and convert to Moore machine Convert NFA with Ɛ a*b* to NFA. Understand 10. Construct NFA for (0 + 1)*101 and Convert to DFA. 11. Construct a mealy machine that takes binary number as input and Understand produces s complement of that number as output.assume the 3 string is read LSB to MSB and end carry is discarded. 1. Explain with the following example the Minimize the DFA. Understand 13. Construct a DFA, the language recognized by the Automaton being L {a n b/n 0}. Draw the transition table. 14. Construct the Minimized DFA 15. Construct the DFA that accepts/recognizes the language L(M) = w {a, b, c}* and w contains the pattern abac }. Draw the

3 transition table. 16. Construct NFA for given NFA with Є-moves 17. Differentiate between DFA and NFA with an example. Understand 18. Construct a finite automaton accepting all strings over {0, 1} having even number of 0 s and even number of 1 s. 19. Construct a Moore Machine to determine the residue mod 5 for each binary string treated as integer. Sketch the transition table Construct the Moore Machine for the given Mealy machine STATE/I a b output q0 q1 q 1 q1 q1 q1 0 q q1 q0 1 Understand 3 Part- C (Problem Solving and Critical Thinking) 1 Construct NFA for (0 + 1)*0(0 + 1)0(0 + 1)* and convert to DFA. Construct NFA for (0 + 1)*010(0 + 1)* and Convert to DFA. 3 Construct NFA with Ɛ for 0*1*1* and Convert to NFA. 4 Construct Mealy Machine for Residue Modulo of 5 for the ternary number system and convert to Moore Machines. 5 Write the DFA that will accept those words from {a, b} where the number of a s is divisible by two and the number of b s is 6 divisible by three. Sketch the transition table of the finite Automaton Construct DFA M. for the given NFA as shown in fig. below UNIT II Part- A (Short Answer Questions) 1. Define Regular Languages. Remember 7. Define Pumping Lemma for Regular Languages. Remember 7 3. Write the applications of pumping lemma for regular languages List any two applications of regular expression. Remember 7 5. Define Context Free Grammars. Remember 8 6. Define Left linear derivation. Remember 7 7. Write regular expression for denoting language containing empty string Differentiate left linear and right linear derivations. Understand 8 9. Write the Context free grammar for palindrome. Remember Define right linear grammars. Remember Define Regular grammars. Remember 7 1. Write regular expressions for the Set of strings over {0, 1} whose last two symbols are the same Define right linear derivation. Remember Define left linear grammars. Remember Write the regular language generated by regular expression (0+1)*001(0+1)* Write the Regular Expression for the set of binary strings Write the derivation of the string aaaa from CFG 8

4 S a S/A A a 18. Write the derivation of the string 110 from CFG S A0/B A 0/1/B B A/ Write the Regular Expression to generate atleast one b over Σ ={a,b} 8 0. Write the Context free grammar for equal number of a s and b s. 8 Part- B (Long Answer Questions) 1. Convert Regular Expression 01* + 1 to Finite Automata. Understand 7. Convert given Finite Automata to Regular Expression using Arden s Understand theorem with an example Construct Right linear, Left linear Regular Grammars for 7 01* Explain Identity rules. Simplify the Regular Expression - Understand 7 Є + 1*(011)*(1*(011)*)* 5. Construct Regular grammar for the given Finite Automata. 7 (a+b)*ab*. 6. Construct Leftmost Derivation., Rightmost Derivation, 8 Derivation Tree for the following grammar S ab ba A a as baa B b bs abb For the string aaabbabbba. 7. Explain the properties, applications of Context Free Languages Understand 8 8. Construct right linear and left linear grammars for given Regular 7 Expression. 9. Construct a Transition System M accepting L(G) for a given Regular Grammar G Discuss the properties of Context free Language. Explain the pumping Understand 7 lemma with an example. 11. Write regular expressions for the given Finite Automata 7 1. Construct a NFA with Є equivalent to the regular expression 10 + ( )0*1 13. Construct Leftmost Derivation., Rightmost Derivation, 7 Derivation Tree for the following grammar G = (V, T, P, S) with N = {E}, S = E, T = {id, +, *(,)} E E+E E E* E E (E) E id Obtain id+id*id in right most derivation, left most derivation 14. Write a CFG that generates equal number of a s and b s Convert G = ( {S},{a},{ S as /a},{s} ) into FA Understand Construct a Regular expression for the set all strings of 0 s and 1 s 7

5 with at least two consecutive 0 s 17. Construct context free grammar which generates palindrome strings ={a,b} 18. Construct equivalent NFA with є for the given regular expression 0*(1(0+1))* Construct the right linear grammar for the following 7 0. Write 1 identity rules for regular expressions 7 Part- C (Problem Solving and Critical Thinking) 1 Convert Regular Expression (11 + 0)*(00 + 1)* to NFA with Ɛ. Understand 7 Convert Regular Expression (a + b)*(aa + bb)(a + b)* to DFA. Understand 7 3 Construct Regular Grammars for Finite Automata 0*(1(0 + 1))*. 7 4 Construct Finite 7 5 Automata for A0 a A1 A1 Construct b left linear grammar for the following 7 UNIT III Part- A (Short Answer Questions) 1. Define Greibach normal form. Remember 9. Define nullable Variable. Remember 8 3. Write the minimized CFG for the following grammar Remember 9 S ABCa bd A BC b B b ε C Đ ε D d 4. Convert the grammar to CNF - S ba/ab A as/a B bs/b. Understand 8 5. Explain the elimination of UNIT production. Understand 8 6. Explain the elimination of useless symbols in productions. Understand 8 7. Define CNF. Remember 9 8. Write the minimization of CFG S a S/A A a B aa Understand 8 9. Define the ambiguity in CFG. Remember What is the use of CNF and GNF Write the minimization of CFG - S as1b S1 as1b/ɛ. Understand 8 1. Write the minimization of CFG - S A A aa/ ɛ. Understand Write the minimization of CFG - S AB / a A a. Understand Write the minimization of CFG - S as/a/c A a B aa C acb. Understand Write the minimization of CFG - S AbA A Aa/ ɛ. Understand 8

6 16. Write the minimization of CFG - S asa S bsb S a/b/ ɛ. Understand Write the minimization of CFG - S A0/B A 0/1/B Understand 8 B A/ Convert the grammar to CNF - S asa/aa S bsb/bb S a/b. Understand Convert the grammar to CNF - S aabb A aa/a B bb/a. Understand 8 0. Define PDA. Remember Define NPDA. Remember 10. Differentiate between deterministic and nondeterministic PDA. Understand Define the language of DPDA. Remember List the steps to convert CFG to PDA. Remember Explain acceptance of PDF by final state. Understand Explain acceptance of PDF by empty stack. Understand Convert the following PDA to CFG δ(q0,b,z0)={q0,zz0) 8. Convert the following PDA to CFG δ(q0, b, z)=(q0,zz) 9. Convert the following PDA to CFG δ(q0, ϵ,z0)=(q0,ϵ) 30. Convert the following PDA to CFG δ(q0,a,z) = (q1,z) 31. Convert the following PDA to CFG δ(q1,b,z)=(q1,ϵ) 3. Convert the following PDA to CFG δ(q1,a,z0)=(q0,z0) 33. Convert the following PDA to CFG δ(q0,0,z0)={q0,xz0) 34. Convert the following PDA to CFG δ(q0,0,x)=(q0,xx) 35. Convert the following PDA to CFG δ(q0,1,x)=(q1,ϵ) 36. Convert the following PDA to CFG δ(q1,1,x) = (q1,ϵ) 37. Convert the following PDA to CFG δ(q1,ϵ,x)=(q1,ϵ) 38. Convert the following PDA to CFG δ(q1,ϵ,z0)=(q1,ϵ) 39. Convert the following PDA to CFG δ(q1,ϵ,z)=(q0,ϵ) 40. Convert the following CFG to PDA S ABC BbB 41. Convert the following CFG to PDA A aa BaC aaa 4. Convert the following CFG to PDA B bbb a D 43. Convert the following CFG to PDA C CA AC 44. Convert the following CFG to PDA S a S/A Part- B (Long Answer Questions) 1. Write a short notes on Chomsky Normal Form and Griebach Normal 9 Form.. Show that the following grammar is ambiguous with respect to the Understand 8 string aaabbabbba. S ab ba A as baa a B bs abb b 3. Use the following grammar : 9 S ABC BbB A aa BaC aaa B bbb a D C CA AC D ε Eliminate ε-productions. Eliminate any unit productions in the resulting grammar. Eliminate any useless symbols in the resulting grammar. Convert the resulting grammar into Chomsky Normal Form 4. Illustrate the construction of Griebach normal form with an example. 9

7 5. Show that the following CFG ambiguous. 8 S icts ictses a C b 6. Discuss the Pumping lemma for Context Free Languages concept with Understand 9 example {a n b n c n where n>=0} 7. Write the simplified CFG productions in S a S1b 8 S1 a S1b/ Є 8. Convert the following CFG into GNF. Understand 8 S AA/a A SS/b 9. Explain unit production? Explain the procedure to eliminate unit Understand 8 production. 10. Explain the procedure to eliminate ϵ-productions in grammar. Understand Convert the following grammar into GNF Understand 8 G=({A1,A,A3},{a,b},P,A) A1->AA3 A->A3A1/b A3->A1A/a 1. Write simplified CFG productions from the following grammar 8 A->aBb/bBa B->aB/bB/ϵ 13. Convert the following grammar into GNF S->ABA/AB/BA/AA/B A->aA/a B->bB/b Understand 8 Part- C (Problem Solving and Critical Thinking) 1 Construct PDA for equal number of x s and y s 10 Convert the following grammar Understand 9 into GNF A1 A A3 A A3 A1 /b A3 A1 A /a 3 Construct DPDA for L = { W#W R /W ϵ ( X + Y)*} 10 4 Convert the following PDA to CFG δ(q0,0,z0)={q0,xz0) δ(q0,0,x)=(q0,xx) δ(q0,1,x)=(q1,ϵ) δ(q1,1,x) = (q1,ϵ) δ(q1,ϵ,x)=(q1,ϵ) δ(q1,ϵ,z0)=(q1,ϵ) Understand and 5 Write the PDA that accepts the language{a^m b^n/n>m} Design a PDA for the following grammar S->0A A->0AB/1 B->1 7 Convert the following PDA to CFG M=({q0,q1},{a,b},{z0,za},μ,q0,z0,Ф) δ is given by, δ(q0,a,z0)=(q0,zz) δ(q0,a,z)=(q0,zz0) δ(q0,b,z)=(q1,ϵ) δ(q1,b,z)=(q1,ϵ) δ(q1,ϵ,z0)=(q1,ϵ) UNIT - IV Create 10 Understand and 11 Part- A (Short Answer Questions) 1. Define Turing Machine 1. Explain the moves in Turing Machine. Understand 1 3. Define an Instantaneous Description of a Turing Machine. Remember 1 4. Define the Language of Turing Machine. Remember 1 5. List types of TM. Remember 1 6. Define Computable Functions by Turing Machines. Remember 1 7. Write the difference between Pushdown Automata and Turing 1

8 Machine. 8. Explain Church s Hypothesis. Understand 1 9. Define Context sensitive language. Remember Define multi head Turing Machine. Remember Define multi dimensional Turing Machine. Remember 1 1. Define multiple tapes Turing Machine. Remember Define Recursive languages. Remember Define Recursively enumerable languages. Remember Define Two way infinite Turing Machine. Remember Define Non deterministic Turing Machine. Remember Define Counter machine. Remember Explain the model of Turing machine. Remember Construct Turing Machine for 1 s complement for binary numbers. Remember 1 0. Differentiate Recursive languages and Recursively enumberable languages. Part- B (Long Answer Questions) Remember 1 1. Define a Turing Machine. With a neat diagram explain the working of Remember 1 a Turing Machine.. Differentiate Turing Machine with other automata Construct a Transition diagram for Turing Machine to accept 1 the following language. L = { 0 n 1 n 0 n n 1} 4. Construct Transition diagram for Turing Machine that accepts the 1 language L = {0 n 1 n n 1}. Give the transition diagram for the Turing Machine obtained and also show the moves made by the Turing machine for the string Construct a Transition diagram for Turing Machine to accept the 1 language L= { w#w R w ϵ ( a + b ) *} 6. Write short notes on Recursive and Recursively Enumerable 1 languages. 7. Write the properties of recursive and recursively enumerable 1 languages. 8. Construct a Turing Machine to accept strings formed with 0 1 and 1 and having substring Construct a Turing Machine that accepts the language 1 L = {1 n n 3 n n 1}. Give the transition diagram for the Turing Machine obtained and also show the moves made by the Turing machine for the string Define Linear bounded automata and explain its model? Explain the power and limitations of Turing machine. Create 1 1. Construct Transition diagram for Turing Machine - L={a n b n c n /n>=1} Construct a Transition diagram for Turing Machine to implement 1 addition of two unary numbers(x+y). 14. Construct a Linear Bounded automata for a language where 1 L={a n b n /n>=1} 15. Explain the types of Turing machines Write briefly about the following 1 a)church s Hypothesis b)counter machine 17. Construct a Transition table for Turing Machine to accept the 1 following language. L = { 0 n 1 n 0 n n 1} 18. Construct a Transition diagram for Turing Machine to accept the 1 language L= { ww R w ϵ ( a + b ) *} 19. Construct Transition table for TM - L={a n b n c n /n>=1} 1 0. Construct a Linear Bounded automata for a language where L={a n b n c n /n>=1} Part- C (Problem Solving and Critical Thinking) 1 Construct a Turing Machine that accepts the language L = {a n b n n 0}. Give the transition diagram for the Turing Machine obtained. 1 1

9 Construct a Turing Machine that gives two s compliment for the 1 given binary representation. 3 Construct a Turing Machine to accept the following 1 language. L = { w n x n y n z n n 1} UNIT - V Part- A (Short Answer Questions) 1. Define Chomsky hierarchy of languages. Knowledge 4. Define Universal Turing Machine Knowledge 1 3. Define Context sensitive language. Knowledge 5 4. Define decidability. Knowledge Define P problems. Knowledge Define Universal Turing Machines Knowledge Give examples for Undecidable Problems Understand Define Turing Machine halting problem. Knowledge Define Turing Reducibility Knowledge Define Post s Correspondence Problem. Knowledge Define Type 0 grammars. Knowledge 4 1. Define Type 1 grammars. Knowledge Define Type grammars. Knowledge Define Type 3 grammars. Knowledge Define NP problems. Knowledge Define NP complete problems Knowledge Define NP Hard problems Knowledge Define undecidability problem. Knowledge Define turing Reducibility. Knowledge List the types of grammars. Knowledge 13 Part- B (Long Answer Questions) 1. Explain the concept of decidable and undecidability problems Understand 1 about Turing Machines.. Write briefly about Chomsky hierarchy of languages Explain individually classes P and NP Understand Write a shot notes on post's correspondence problem and check the following is PCP or not. I A B Explain the Halting problem and Turing Reducibility. Understand Write a short notes on universal Turing machine Write a short notes on Chomsky hierarchy Write a short notes on Context sensitive language and linear bounded 4 automata. 9. Write a short note on NP complete Write a short note on NP hard problems Write a shot notes on post's correspondence problem and check the following is PCP or not. I A B Write a shot notes on post's correspondence problem and check the following is PCP or not. I A B

10 UNIT - V 1 Explain PCP and MPCP with examples. Understand 13 Explain Turing theorem,halting problems, Turing Reducibility. Understand 13 3 Explain Type 3 and Type grammars with example. 4 4 Explain Type 1 and Type 0 grammars with example. 4